MHF4U Grade 12 Advanced Functions – Combining Functions Test

Unit 7: Combining Functions

  • Adding and Subtracting Functions
    • Functions that are added/subtracted are called combined functions.
    • Points on the functions can be added by adding y-coordinates at each point along the x axis of both functions.
    • Same goes for subtracting functions at each point.
    • Domain of the sum or difference is the domain of the functions being added or subtracted.


  • Multiplying and Dividing Functions
    • Function of the form y = f(x) g(x) is the product of f(x) and g(x)
    • Function of the form y = f(x) / g(x) is the quotient of the function f(x) and g(x) where g(x) cannot equal 0.
    • Domain of these combined functions is the domain of the functions being combined.
    • When dividing functions, the denominator has a restriction where it cannot equal 0.


  • Composite Functions
    • You can combine functions using the notation: f(g(x)) where f(x) depends on the answer of g(x). Also known as (f o g)(x).
    • To do this, you must find the value for g(x) then substitute that into f(x) to get your answer.


  • Inequalities of combined functions
    • Similarly to finding inequalities for normal functions, simply move everything to one side, factor then solve. Or graph and see where it meets the criteria.